Mathematics Question and Solution
Calculating the radius of the small inscribed pink circle. Let it be r.
b = ⅕*180(5-2)
b = 108°
b is the single interior angle of the ascribed regular pentagon.
c² = 10²+10²-2*10*10cos108
c = 16.1803398875 units.
d = 108-36
d = 72°
e = 90-72
e = 8°
f²+(0.5*10)² = c²
f² = 16.1803398875²-5²
f = 15.3884176859 units.
tan54 = g/5
g = 6.8819096024 units.
Again, a is the radius of the bigger inscribed circle.
h = 2g
h = 13.7638192047 units.
It implies;
sin18= r/j
j = 3.2360679775r units.
Therefore calculating r, radius of the inscribed small pink circle.
r+j+h = f
r+3.2360679775r+13.7638192047 = 15.3884176859
4.2360679775r = 1.6245984812
r = 1.6245984812/4.2360679775
r = 0.3835156777 units.
